Rolling On One

On Sunday (must have been Sept. 23) we went for a walk sponsored by the Newton Conservators near the Charles with an expert on ferns. He showed us, and explained how to identify, twelve species of ferns which are reasonably common in the area. There are almost another dozen species found in Newton, but this was one of the best places for finding a lot of different kinds in a small area.

So we saw Sensitive Fern, Lady Fern, Royal Fern, Hay-Scented Fern, Marsh Fern, Cinnamon Fern, Interrupted Fern, Spinulose Wood Fern, New York Fern, Ostrich Fern, hm, and two others that I can’t remember at the moment. Maybe one was another kind of Wood Fern, and maybe he was counting the horsetails. That would make a dozen.

Can I recognize them now, two weeks or so later? I’ve been checking when I walk in Cutler Park, and I don’t really think I remember more than four of them. Darn.

We spent a quiet day at home Sunday finishing the jigsaw puzzle we had started the evening before —

— it’s one of those old Springbok puzzles with pieces so thick and precisely cut that you can pick the whole thing up when it’s finished —

— picking apples, because the ones that are ripe now will be past the time for picking next time we’re here; there were a lot, and there are a lot left on the heritage tree, and the red delicious and baldwin aren’t ready to pick yet but there aren’t many apples on either of them, but how about these? They look better here than they do close up; you can’t see the spots here, and I posed the good sides facing the camera. Many are fine for eating out of the hand, but you want to watch where you bite.

Notice the different colors. The heritage apples (in the two mass-produced baskets) are more toward orange in color and the macintosh (in the nice handmade basket we got in Orono last December) are more towards violet. My memory from last year is of the heritage being somewhat yellow, like golden delicious. I was very surprised at how red they are.

We tried fishing for a while at the Heath causeway but didn’t catch anything. The furnace guy had told us on Friday that his grandfather (I think that’s who — some ancestor, let’s go with grandfather) had built the causeway, piling rocks on the ice during the winters. They would of course fall in when the ice thawed. That’s a lot easier than trying to drop a big rock off a boat!
And here was part of supper. The brussels sprouts are from the Newton farmers’ market. Arlene says there were a lot of people walking around the market carrying stalks of sprouts like this. She didn’t know if it was because more people than we realized like brussels sprouts or just because they’re so interesting. The green pepper is from our garden in Casco.

Arlene was over to walk around Cutler Pond one day last week, I think Wednesday. We saw two ospreys soaring over the pond. The next day when I walked I saw one osprey in a dead tree near the far end of the pond. I was looking for a kingfisher that I had heard in that area, and saw the osprey before I found the kingfisher. I saw the osprey again today in the same tree. I don’t know if it’s the same bird or just a tree that has everything any osprey could ask for.

There has been at least one great blue heron either in the pond or the river every day I’ve walked the last couple of weeks, and a kingfisher pretty frequently. I sometimes hear the kingfisher but don’t see it.

On Saturday we went for a hike on the other side of Bridgton. There’s a lot of construction going on in Bridgton this year. Everyone we spoke with was excited about the new Hannaford’s supermarket that opened a year and a half ago, and the big Hancock Lumber yard that opened was welcome, but both of those were highway sorts of businesses, not downtown. The current construction is downtown: rebuilding the Magic Lantern cinema, and expanding Reny’s department store. Both of those should help keep business in town and encourage foot traffic to the rest of the stores in town. We hadn’t been in Bridgton for a while, and the progress on both of those buildings was impressive. We went into Reny’s while we were there. I got a new pair of jeans, because the ones I had been wearing were turning into rags. I mean, one patch on a knee is New England thriftiness, but two holes on the other leg is turning into rags.

We went over to Denmark to find the trail up Pleasant Mountain that the Loon Echo Land Trust was so excited about having preserved. It’s off Mountain Road, off Hio Ridge Road. There was a small parking area on the opposite side of the road from this trailhead:

It was a good clearly marked trail, with blue dots painted on rocks near the bottom and blue rectangles painted on trees farther along. A couple of hundred yards along the trail here was a little kiosk with a big map of the trails on a bulletin board and a pocket of trail maps that you could take. We had left one in the car, so I took one and returned it when we came back. We met several parties of people walking down the mountain as we were climbing. Somewhere along the way was this cleft rock —

…and up as far as we went, about 1.1 miles that took us about 50 minutes to walk, was a wooden grave marker —

… and a magnificent view over Moose Pond.

We were a little disappointed that the foliage wasn’t prettier. A lot of the woods are conifers here.

On our way back we ran into one group of people who were walking up to watch the sunset from the top. They’re more comfortable hiking in the dark than we are! We were beginning to be concerned about getting back before dark.

Here are some trucks that were on display at the fair. First, this lumber delivery truck from Chebeague Island. Chebeague Island is in Casco Bay (no relative of the town of Casco) off Portland. It was in the news a few years ago because its residents convinced Nabisco to continue making Pilot Crackers, something like oversize oysterette crackers, which are considered absolutely essential to proper clam chowder. At least they were fifty years ago and nowadays on Chebeague Island, which might have been the only place where a significant number of them were still being sold. At any rate, Nabisco first announced it would discontinue them, then capitulated to the protest and sent a boat loaded with them over with lots of hoopla.

Here’s a lovely horse-drawn milk wagon:

This woodie pickup truck didn’t have any label.

And finally, here’s the Royal River Band Wagon. It’s roped off so you can’t jump on the bandwagon, but a band wagon it is. That looked like some sort of power pipe organ designed to imitate a brass band.

I took a vacation day Friday and we spent a three day weekend in Maine.

There was a little unfinished business with the roof, or at least with the skylights; the finish carpentry, the trim around the bottom of the skylights, wasn’t done. Porky was going to come in the morning to do that, and to pick up a lot of tools he had left in the garage. We also figured that it would be a good time to get the oil burner annual service done. So we expected two people to come over between 8 and 9 in the morning. When Porky told us when he would be there, he forgot that school would have started and they would have to drop off a kid at school, so it turned out that he was later than we expected him. But the oil burner guy was on time, so we hadn’t wasted getting up at a reasonable hour.

The weather wasn’t promising, showers on and off, mostly on, in the early morning, tapering off to mostly off in the late morning. By the time the carpentry work was done (and it took extra long because the wood was too thick, so you couldn’t get the screen out of the skylight, and Porky took it back to his house to cut down on his table saw) the sun was out and the day looked pretty good. We decided to go to the Cumberland County Fair for the afternoon and stop at Lowe’s in Windham on the way home to get the crank for the skylight that you can reach by hand.

The Cumberland Fair is much smaller than the Fryeburg Fair, maybe a quarter as big. It has most of the attractions, just not as much of anything. We went to the Fryeburg Fair on Saturday last year, and this was Friday, so it’s not really a good comparison; but this was so much less crowded, and so much less traffic, that we liked it a lot better. It’s pretty close to Portland, so it probably gets quite crowded on weekends.
We went over to look at the trotting races first. I’ve heard people say that in Massachusetts the so-called “agricultural fairs” are just an excuse to have horse racing, and maybe there’s something to that. At Cumberland there weren’t all that many people watching the racing compared to the overall attendance. When we left a woman working at the gate told us that they used to have racing at night at Cumberland, but they stopped it because there were too many problems, drinking and rowdiness.

But whatever, Arlene and I had never seen a trotting race before (and only one other horse race, at Churchill Downs, in 1984). We got there a few minutes before a race was about to start, and sulkies were warming up on the track. Now I have to tell you, I’m partial to sulkies because when I was a kid, Wheaties cereal boxes used to have model vehicles on the back you could cut out and assemble (add a piece of spaghetti for the axles), and one was a sulky. After making a few of those, I’ve always liked seeing real ones.

This race was two laps around a half-mile track. It’s not clear to me how the start really works; there was a truck towing the starting gate and when all the horses were pretty close behind it the announcer said something like, “They’re in motion!”, the truck and gate pulled way ahead and off to the side, and the race was on. I was probably too concerned with getting a few pictures and not enough with really watching, but here are the pictures:

Gotta have two pictures, because as I said, the race was two laps.

There seemed to be more people watching the draft horse pulling contest than the horse racing. When we came in the announcer was saying “This round, 3400 pounds.” There was a sort of sled with recycled railroad track for runners and concrete blocks, not the little ones used in buildings but big blocks of concrete that probably weighed 200 pounds each, stacked on it. A tractor would tow the sled to the starting line, people would rake the ground rough where the previous contestant had smoothed it out with the sled so everyone had a similar surface to contend with, then the horse’s handlers would back the horse up to the sled, hook its harness to the front end of the sled, and get the horse to move. It looked as though five or six feet was as far as they needed to go, because if it got much beyond that the handlers would let the horse stop and the announcer would say, “All the way! Good job!” If it didn’t get that far, the announcer would say “Twenty-nine inches,” or however far it was. As far as we could tell, the idea was that all the horses that pull the load “All the way!” get to go on to the next round, probably with 200 more pounds. The last horse to pull the load all the way, or the one that goes farther in the last round if none of them pull it all the way, wins. It was a little hard to believe that both the pulling and the racing were about horses, but then, Olympic weight lifting and sprinting are both about humans.

New England fairs, at least in autumn, seem to include giant pumpkin contests. We saw giant pumpkins in Fryeburg last year. The TV news reports of the Topsfield fair, the one closest to Boston, always include shots of giant pumpkins (maybe that’s because they hold very still to be photographed.) Here are some from Cumberland:

Each of those is probably over three hundred pounds, and not much use for anything except entering in the contest.

The ferris wheel was very pretty from the opposite side of the racetrack. Many of the most interesting exhibit buildings, such as a museum of antique farm equipment, a blacksmith shop, and an exhibit about making maple syrup, were over here.

We had supper at a restaurant run by one of the local churches; it seemed to offer our best chance to get something that wasn’t fried. The special was barbecued chicken, which was OK and quite reasonably priced for fair food, but not as good as I make on the grill. We split a piece of custard pie, which was quite good. We sat at the counter, hoping to hear more of the general conversation than we would at a table. A lot of the customers did seem to know each other and the people running the place. Unfortunately, I can’t recall any of it any more.

The midway was as gaudy as you could ask for.

There was a nice display of antique trucks in a building on the far side of the midway. I’ll put those pictures in a separate post.

Don’t know about you, but I’ve seen several emails over the last couple of weeks with a number trick that goes something like this:

*****************************************

Write down how many times a week you would like to dine in a restaurant, at least 1 but less than 10 times.

Double that.

Add five.

Multiply by fifty.

If you’ve had your birthday already this year, add 1757. If not, add 1756.

Subtract the year you were born.

The answer is a three digit number. The first digit is the number of restaurant meals you started with. The last two digits are your age.

******************************************

Amazing? Not particularly. As your friendly local internet mathematician, I’d like to show you how this trick works. Once you know, you can figure out how a zillion things like it work.

First of all, if you don’t know how old someone is but you know their date of birth, you can figure out their age by subtracting the year they were born from the current year, if they’ve had their birthday by now, or from last year, if they haven’t had their birthday yet. Think if someone had a baby last year — how old is it? If it’s had its first birthday by now, it’s one year old. If not, it’s not a year old yet. OK. So the trick is a tricky way to get you to subtract the year you were born from 2007 or 2006, without your knowing that’s what you’re doing.

The way we’re going to do that is to hide the 2007 or 2006 by building it up out of other numbers which don’t look like it and which we can get rid of later. Fortunately, numbers are totally predictable. Remember hearing about some things like associative and commutative properties? They really just mean that if you do the arithmetic right, you can undo things later and be confident you’ll get back what you expect. Algebra, I know lots of people hate hearing the very word and if you’re one of them you’re excused from reading the rest of this post, is just a way of doing arithmetic without knowing what the numbers are, so you can keep track of the underlying structure. So lets roll up our sleeves and do some algebra. It really won’t hurt.
Since I don’t know how many times a week you want to dine in a restaurant, I’m going to say,

“Let x = the number of times a week you want to dine in a restaurant”. So for step 1, you wrote x.

The key thing that my high school math teachers said over and over and over is “Let x = the NUMBER of something”. I don’t know how to do arithmetic or algebra with “how old you are” or “how many times”, or that kind of stuff. Only with NUMBERS. Sorry for shouting there, but it’s THE KEY THING. A NUMBER. Any time you do a word problem in algebra, let x = A NUMBER!
Double that. That means multiply it by two. In algebra, we write that as 2x.

Add five. In algebra, we just write down the arithmetic problem and don’t worry that we don’t know what it comes out to: 2x + 5.

Multiply by fifty. Now we need to use the distributive property of numbers, but it even makes sense. Someone I used to teach with (his last name was Natapof, and I forget the first name) explained it like this:

“Suppose you had a bunch of eggs. You could pack them in cartons of a dozen each, and you’d have some left over. Now, suppose you had twice as many to start with. That would make twice as many dozens, and twice as many leftovers. Twice as many eggs is twice as many dozens plus twice as many leftovers.”

Now, if you had fifty times as many, that would make fifty times as many dozens and fifty times as many leftovers. That’s the distributive property at work. So to multiply by fifty, we write 50(2x + 5), but that’s 50 times 2x plus 50 times 5, or 50 times 2x plus 250. Now the associative property of multiplication says that 50 times 2x is equal to 50 times 2, all times x. 50 times 2 is 100, so we’re up to 100x for that part, or 100x + 250 all together.

The next thing was to add 1757. So we have 100x + 250 + 1757. The associative property of addition says that we’ll have the same thing if we add 100x + 250 first and then add 1757, or if we add 100x to what we get when we add 250 and 1757. Since we can do the arithmetic for 250 + 1757 and just get a plain number, we might as well do that. Lo and behold, we get 2007. So the whole thing is 100x + 2007 (or 100x + 2006 if you haven’t had your birthday this year yet.)

By now I’m getting sick of explaining, so I’m just going to say that at this point you can probably see that after you subtract the year you were born from whatever you had there, you have 100x + your age. The 100x is just the first digit of the 3-digit number.

The good thing about algebra is that it doesn’t have all those words in it. If you’re comfortable using algebra, which is a different thing from “if you know algebra”, you would just write

Let x = the number of restaurant meals

2x

2x + 5

50(2x + 5) = 100x + 250

100x + 250 + 1757 = 100x + 2007

100x + 2007 – year_of_birth = 100x + (2007 – year_of_birth) = 100x + age

So there you are. I AM comfortable using algebra, so whenever I get one of those emails, I don’t say, “amazing!,” I get out a pencil and paper, do a few lines of algebra, and say, “ho hum, another of those.”

Signed,

Your Friendly Local Internet Mathematician

I had an extra good bike ride to work on Wednesday (Sept 12 — I’m a week behind posting this). Traffic was a little backed up at the end of Parker, so I went right on Dedham, down Rachel, out Winchester, and through Nahanton Park to avoid a probable backup at the Wells Ave/JCC light.

When I got out to Nahanton St, there were two bicyclists getting set to leave that little parking area on a ride. They were dressed like serious bicyclists, in spandex tops and shorts, and were on real road bikes, with dropped handlebars and skinny tires. I ride a hybrid bike, with upright handlebars and medium wide tires that will hold up on the grass and gravel paths through the park, or on easy trails through the woods when I used to ride through Prospect Hill Park. I called to the other cyclists, “I’d say ‘passing on the left’, except that you’d pass me in five seconds.” When they turned to look, one of them seemed to recognize me. Holy smokes! Carol Marton, Koleinu director! So we had a nice little visit (including a hug). “Are you living in the park now?” she asked. “Yes, in one of those shelters behind the community gardens,” I said. She’d like me to come back to Koleinu, but I need a couple of weekday evenings at home.

I’ve been bringing my camera along to work, and along on my lunchtime walks, in the hope of seeing that northern water snake and getting a picture. Today, on the opposite side of the pond from where I’ve seen them before, there was a snake right in the path. I stopped short a few yards from it, got out the camera, and started taking pictures. Here’s the best one:

As I was watching it, a woman whom I’ve seen walking many days came along from the opposite direction, plugged in to her iPod. I held out my hand like a crossing guard for her to stop — I didn’t want to shout and alarm the snake — but she didn’t notice until she was even with the snake. I pointed down to it, and she gasped at finding herself about three feet from it. I told her all about having looked up “New England snakes” on the net after the first time I saw one of these, reassured her that it wasn’t venomous and that poison ivy was a bigger danger in New England than snakes, and showed her some poison ivy that was a few steps further down the path. Meanwhile, a jogger came up from behind me and ran on past the snake, completely oblivious to it.

Here’s a blowup of the head of the snake, just so you can see the pattern on it and the scales. The pattern actually shows up better in the photo than it did in the field.

First, here’s something the roofers used to clean up. They had left a lot of stuff in our garage to pick up after the finish carpentry is all done. They encouraged us to use this gizmo, which is a magnetic sweeper. The idea is that it will pick up nails, staples, and other ferrous-metal scrap from the ground. When you have enough collected, you can pull up the small handle and the scrap should fall off the bottom.

We ran it along the first fifty feet or so of the driveway and all around the house. It made a nice clicking sound every time a nail or staple jumped up and stuck on it, but it turned out that there were fewer things stuck to it than there had been clicks. It seemed that as you ran the sweeper over more grass the nails would dislodge and click back on. We did pick up several handfuls of nails and staples with it, though, even after the roofers had gone over everything.

Then there was a yard sale that we stopped at, along the top of the ridge on Mayberry Hill Road. The people at the preschool had told us that we could walk up the field on the other side of the property that was holding the yard sale, so we wanted to talk to the people there to see if it was all right to walk there anyway. I saw a box of stamps for tooling leather, a complete alphabet set, and got that. Then my eye fell on a bandsaw. I’ve been wanting one for cutting up turning stock. It’s a lot safer than a table saw for that application because it doesn’t kick back or throw cutoff wood across the room. The guy who was selling it said he had bought it new but never used it. It took a lot of fiddling with before it was ready to go. The blade needed to go back on the wheels, one wheel needed a friction belt to drive the blade (I used some non-slip material like drawer lining stuff), the upper wheel needed to be reconnected to the tension adjustment knob, and every possible adjustment needed to be readjusted. It still needs to be bolted down, or lagscrewed down, to the workbench before I’m going to saw any wood on it.

I think this is as small a bandsaw as they come. At any rate, it takes the smallest blade listed on a website of bandsaw parts.